Respuesta :
Answer:
The standard deviation of the sample is 2.55 gigabytes
Step-by-step explanation:
Here we have the responses as follows;
Storage space usage on their computer [tex]x_i[/tex]
The number of respondents or sample size, n = 5
[tex]x_i[/tex] [tex](x_i - \bar x)[/tex] [tex](x_i - \bar x)^{2}[/tex]
4 -4 16
8 0 0
8 0 0
9 1 1
11 3 9
∑ 40 26
The sum = ∑X = 4 + 8 + 8 + 9 + 11 = 40
The mean = (The sum)/(The count) = 40/5 = 8
Formula for population standard deviation is;
[tex]\sigma = \sqrt{\frac{\Sigma (x_i - \mu)^2}{n } }[/tex]
Where:
σ = Population standard deviation
μ = Population mean
Since we are dealing with only 5 out of her hundreds of coworkers we are dealing with a sample therefore;
The formula for sample standard deviation is;
[tex]s = \sqrt{\frac{\Sigma (x_i - \bar x)^2}{n - 1} }[/tex]
Where:
s = Sample standard deviation
n = Sample size
[tex]x_i[/tex] = Each value of the sample
[tex]\bar x[/tex] = Sample mean
We find each value of [tex](x_i - \bar x)[/tex] by subtracting the x values from the mean, 8, as in the table above, next we find [tex](x_i - \bar x)^{2}[/tex] by squaring the [tex](x_i - \bar x)[/tex].
Next, we find the sum of the differences from the mean square values from the table after which we divide by n - 1, to get [tex]{\frac{\Sigma (x_i - \bar x)^2}{n - 1} } = \frac{26}{5 - 1} = \frac{26}{4} = 6.5[/tex]
We find the root of the result which gives us the standard deviation hence
√6.5 = 2.5495.
Standard deviation, s = 2.5495 ≈ 2.55 to two significant places of decimal.
